The rope

A rope is made of five thin strands twisted together. One strand alone can carry at most twenty kilograms.

Rope: $5$ strands. One strand carries at most $20$ kg.

Strands $n=5$, each $w\le 20$ kg.

The strands share the load. If a bucket of ninety kilograms hangs from the rope, each strand carries eighteen kilograms, which is less than twenty, so the rope holds.

A load of $90$ kg is shared: $90÷5=18$ kg each, and $18\le 20$, so the rope holds.

$W=90$, $90/5=18\le 20$ ✓

Now a sharp stone cuts one strand. Ninety kilograms are shared by four strands, and each carries twenty-two and a half, which is more than twenty. The next strand snaps, then the next, and the rope falls.

One strand cut: $90÷4=22.5>20$, so a strand snaps. Then $90÷3=30>20$, and so on until it falls.

Cut: $90/4=22.5>20$ ✗, $90/3=30>20$ ✗

With a bucket of eighty kilograms, four strands would carry exactly twenty each, right at their limit, and the rope would hold, only just. In general a rope holds when the load divided by the number of strands is at most twenty.

A load of $80$ kg: $80÷4=20\le 20$, it holds, only just. The rule for $n$ strands and a load $W$ is $\frac{W}{n}\le 20⟺n\ge \frac{W}{20}$.

$80/4=20\le 20$ ✓; $\frac{W}{n}\le 20⟺n\ge \frac{W}{20}$

So for ninety kilograms you need at least four and a half strands, which means five, with none to spare. Add one spare strand: with six, after one is cut, five still carry eighteen each, and the rope stays up. A spare strand is what saves a rope.

For $W=90$ we need $n\ge \frac{90}{20}=4.5$, so $n\ge 5$. With $6$ strands and one cut: $90÷5=18\le 20$, the rope holds.

$n\ge \frac{90}{20}=4.5$; $n=6$ and one cut: $90/5=18\le 20$ ✓